Question

Solve for x if = (4x+39)DE=(4x+39). If necessary, round your answer to the nearest tenth.

Answer 1

Given that,

In circle,

measure of angle DGE is 52 degrees

`m(arcDE)=(4x+39)\degree`

To solve for x,

we know that,

The angle formed by the two secants that intersect on the circle is half of the intercepted arcs.

Using this we get,

`\angle DGE=(1)/(2)(arc(DE))`

Substitute the values we get,

`52\degree=((4x+39)\degree)/(2)`
`104=4x+39`
`4x=104-39`
`4x=63`
`x=(63)/(4)`
`x=15.75`

Round the answer to the nearest tenth.

`x=15.8`

Answer is:

`x=15.8`